Finite Group Databasebeta

← #21434784

Subgroups — #21434784

Order 7552.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838026C211yesmaximal, characteristic, complemented
2#16838008C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837759C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837656C211yesmaximal, characteristic, complemented
7#16837649C211yesmaximal, characteristic, complemented
8#16837639C211yesmaximal, characteristic, complemented
9#16837632C211yesmaximal, characteristic, complemented
10#16837513C211yesmaximal, characteristic, complemented
11#16837501C211yesmaximal, characteristic, complemented
12#16837489C211yesmaximal, characteristic, complemented
13#16837484C211yesmaximal, characteristic, complemented
14#16837359C211yesmaximal, characteristic, complemented
15C59×#501C211yesmaximal, characteristic, complemented
16C2×#11745660C2211yescharacteristic
17C2×#11745660C2211yescharacteristic
18C2×D472C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273724C2211yescharacteristic
23#14273722—21no—
24#14273716—21no—
25#14273715C2211yescharacteristic
26#14273712—21no—
27#14273712—21no—
28#14273712—21no—
29#14273707C2211yescharacteristic
30#14273703—21no—
31#14273702—21no—
32#14273702—21no—
33#14273702C2211yescharacteristic
34#14273702C2211yescharacteristic
35#14273702C2211yescharacteristic
36#14273692C2211yescharacteristic
37#14273689C2211yescharacteristic
38#14273689C2211yescharacteristic
39#14273689C2211yescharacteristic
40#14273684C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273650C2211yescharacteristic
43#14273647C2211yescharacteristic
44#14273647C2211yescharacteristic
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47#14273647C2211yescharacteristic
48#14273647C2211yescharacteristic
49#14273637C2211yescharacteristic
50C4×C59⋊C8C2211yescharacteristic
51C8×Dic59C2211yescharacteristic
52C4⋊Q8×C59C2211yescharacteristic
53#125×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#106×C59C2211yescharacteristic
57#106×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59—21no—
60C2×D236—21no—
61C2×D236—21no—
62C2×D236—21no—
63C2×D236—21no—
64C2×D236—21no—
65C2×D236C2311yescharacteristic
66C2×D236C2311yescharacteristic
67C2×D236C2311yescharacteristic
68C2×C4×D59—21no—
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59C2311yescharacteristic
72C2×Dic118C2311yescharacteristic
73C2×C8×C59C2311yescharacteristic
74C2×C8×C59C2311yescharacteristic
75C4⋊C4×C59—21no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59C2311yescharacteristic
79C4⋊C4×C59C2311yescharacteristic
80C4⋊C4×C59C2311yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C42×C59C2311yescharacteristic
83(C2×D59)⋊C4—21no—
84(C2×D59)⋊C4—21no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4D411yescharacteristic
93(C2×D59)⋊C4D411yescharacteristic
94C4⋊Dic59—21no—
95Dic59⋊C4—21no—
96Dic59⋊C4D411yescharacteristic
97Dic59⋊C4D411yescharacteristic
98C4×Dic59—21no—
99C4×Dic59C2311yescharacteristic
100C2×C59⋊C8C2311yescharacteristic
101C2×C59⋊C8C2311yescharacteristic
102D472—22no—
103D472—22no—
104#11745660—22no—
105#11745660—22no—
106#11745659—22no—
107C8×D59—22no—
108C22×D59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59C2×D411yescharacteristic
112Q8×C59—81no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59C2×D411yescharacteristic
118C2×C4×C59C2×D411yescharacteristic
119C2×C4×C59C2411yescharacteristic
120C2×Dic59—21no—
121C2×Dic59C2×D411yescharacteristic
122C2×Dic59C2×D411yescharacteristic
123C2×Dic59C2×D411yescharacteristic
124D236—21no—
125D236—21no—
126D236—21no—
127D236—21no—
128D236—21no—
129D236—21no—
130D236—81no—
131D236—81no—
132D236—81no—
133D236—81no—
134D236—81no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—81no—
138C4×D59—81no—
139C4×D59—81no—
140Dic118—21no—
141Dic118—21no—
142C8×C59#4112yes—
143C8×C59#4112yes—
144C59⋊C8—21no—
145C59⋊C8—21no—
146C22×C59C22×D411yescharacteristic
147C2×D59—21no—
148C2×D59—21no—
149C2×D59—21no—
150C2×D59—41no—
151C2×D59—41no—
152C2×D59—41no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—41no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—41no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59C2×#4111yescharacteristic
166C4×C59C2×#4111yescharacteristic
167Dic59—21no—
168Dic59—21no—
169Dic59—21no—
170Dic59—41no—
171#3179—591nomaximal, Sylow
172C2×C59#53211yescharacteristic
173C2×C59#57611yescharacteristic
174C2×C59#57711yescharacteristic
175D59—41no—
176D59—81no—
177D59—81no—
178D59—81no—
179#542—591no—
180#540—591no—
181#501D5911yescharacteristic, complemented
182#496—591no—
183#488—591no—
184#486—591no—
185#469—591no—
186#468—591no—
187#466—591no—
188#465—591no—
189#442—591no—
190#440—591no—
191C4×SD16—591no—
192C4×D8—591no—
193#405—591no—
194C59#317911yescharacteristic, complemented, Sylow
195C2×SD16—591no—
196C2×SD16—591no—
197C2×D8—591no—
198C2×D8—591no—
199C2×M16—591no—
200C22×C8—591no—
201C4⋊Q8C2×D5911yescharacteristic
202#127—591no—
203#126—1181no—
204#125C2×D5911yescharacteristic
205#124—591no—
206#124—1181no—
207#123—1181no—
208#123—1181no—
209#123—1181no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—591no—
214#121—591no—
215#121—1181no—
216#121—1181no—
217C4×Q8—591no—
218C4×D4—591no—
219C4×D4—591no—
220C4×D4—591no—
221#117—591no—
222#107C2×D5911yescharacteristic
223#107C2×D5911yescharacteristic
224#106C2×D5911yescharacteristic
225#106C2×D5911yescharacteristic
226#103—591no—
227#103—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231#102—591no—
232#102—591no—
233#102—591no—
234#97—591no—
235#97C2×D5911yescharacteristic
236C4×C8—591no—
237C4×C8—591no—
238C2×Q8—21no—
239C2×Q8—591no—
240C2×D4—591no—
241C2×D4—591no—
242C2×D4—591no—
243C2×D4—1181no—
244C2×D4—1181no—
245C2×D4—1181no—
246C2×D4—1181no—
247C2×D4—1181no—
248C22×C4—591no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4—1181no—
252SD16—1182no—
253SD16—1182no—
254D8—1182no—
255D8—1182no—
256M16—1182no—
257C2×C8—591no—
258C2×C8—591no—
259C2×C8—1182no—
260C2×C8C22×D5911yescharacteristic
261C2×C8C22×D5911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4C22×D5911yescharacteristic
270C4⋊C4C22×D5911yescharacteristic
271C4⋊C4C22×D5911yescharacteristic
272C4⋊C4C22×D5911yescharacteristic
273C22⋊C4—591no—
274C22⋊C4—591no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C42—591no—
285C42—1181no—
286C42C22×D5911yescharacteristic
287C23—591no—
288C23—1181no—
289C23—1181no—
290C23—1181no—
291Q8—81no—
292Q8—1181no—
293Q8—1181no—
294D4—1181no—
295D4—1181no—
296D4—1181no—
297D4—1181no—
298D4—1181no—
299D4—1181no—
300D4—4721no—
301D4—4721no—
302D4—4721no—
303D4—4721no—
304D4—4721no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—591no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4D4×D5911yescharacteristic
319C2×C4D4×D5911yescharacteristic
320C2×C4C23×D5911yescharacteristic
321C8—1181no—
322C8—1181no—
323C8#1174568912yes—
324C8#1174568912yes—
325C22—1181no—
326C22—1181no—
327C22—1181no—
328C22—2361no—
329C22—2361no—
330C22—2361no—
331C22—2361no—
332C22—2361no—
333C22—2361no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—1181no—
345C4—1181no—
346C4—1181no—
347C4—2361no—
348C4C2×#1174568911yescharacteristic
349C4C2×#1174568911yescharacteristic
350C2—4721no—
351C2—4721no—
352C2—4721no—
353C2—2361no—
354C2#1683795311yescharacteristic
355C2#1683820611yescharacteristic
356C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#501C2
socleC22×C59C22×D4
hypercenter#501D59
hypocenterC59#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16838026C2semidirect
2. #16838008C2semidirect
3. #16837791C2semidirect
4. #16837759C2semidirect
5. #16837750C2semidirect
6. #16837656C2semidirect
7. #16837649C2semidirect
8. #16837639C2semidirect
9. #16837632C2semidirect
10. #16837513C2semidirect
11. #16837501C2semidirect
12. #16837489C2semidirect
13. #16837484C2semidirect
14. #16837359C2semidirect
15. C59×#501C2semidirect
181. #501D59semidirect
194. C59#3179semidirect